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We extend the Minimum Supersymmetry Standard Model by a non-anomalous family(NAF) U(1)'_{NAF} gauge symmetry. All gauge anomalies are cancelled with noadditional exotics other than the three right-handed neutrinos. The FI D-termsassociated with the U(1)'_{NAF} symmetry lead to additional positivecontributions to slepton squared masses. In a RG invariant way, this thussolves the tachyonic slepton mass problem in Anomaly Mediated SupersymmetryBreaking. In addition, the U (1)'_{NAF} symmetry naturally gives rise to thefermion mass hierarchy and mixing angles, and determines the mass spectrum ofthe sparticles.

Lifting Slepton Masses with a Non-universal, Non-anomalous U(1)'_{NAF} in Anomaly Mediated SUSY breaking